# Limit theorems for pseudo sum of discrete distributions

## TL;DR

This paper introduces associative Look-Up Tables to accurately determine pseudo sums of discrete distributions, characterizes the limit distributions in pseudo-summation schemes, and explores conditions for domain attraction of stable distributions.

## Contribution

It presents a novel approach using associative Look-Up Tables for pseudo sums and fully characterizes limit distributions and domain attraction conditions.

## Key findings

- Set of limit distributions in pseudo-summation schemes described
- Stable and infinitely divisible distributions characterized
- Conditions for domain of attraction of stable distributions provided

## Abstract

In this article we introduce associative Look-Up Tables. With their help, pseudo sums are correctly determined. The set of limit distributions in a pseudo-summation scheme of i.i.d. random variables is described. Also, two special cases that are similar to the classical sum and maximum operations are considered. In both situations, the set of stable distributions and the set of infinity divisible distributions are fully described. In addition, necessary and sufficient conditions for random variable to belong to the domain of attraction of stable random variable are introduced.